This application is based on application No. 11-164823 filed in Japan, the content of which is hereby incorporated by reference.
1. Field of the Invention
The present invention relates to a three-dimensional machining method for machining a workpiece three-dimensionally with a machine tool such as a milling cutter, and more particularly to a processing control for defining a surface to be machined and determining paths of a cutting tool to machine the surface.
2. Description of Related Art
Recently, computerized three-dimensional machining of a metal workpiece has been developed for practical use. The three-dimensional machining is generally performed based on either paths of the working end of a ball tip of a cutting tool or paths of the center of the ball tip of the cutting tool.
In either method, conventionally, a plurality of surfaces to be machined are defined individually, and continuous surfaces are machined by transfer cutting. For example, as FIGS. 7a and 7b show, three continuous surfaces #i, #j and #k are defined individually (in individual coordinate systems (u, v)) and are machined continuously by transferring a cutting tool from a path to machine the surface #i to a path to machine the surface #k and then to a path to machine the surface #j. In the transfer cutting, generation of tool paths is sometimes performed based on a direction xcex3 which does not reflect the characteristics of the surfaces. In this case, the transfer cutting is not in accordance with the characteristics of the surfaces, and the cutting may be rough or may be unnecessarily fine and wasteful. Further, for transfer cutting, a large volume of processing to avoid interference of the cutting tool is necessary, which takes a lot of time.
In order to solve the above problems, the applicant disclosed, in U.S. Pat. No. 5,515,290, a three-dimensional machining method wherein a plurality of curved surfaces which have distinct characteristics are defined as a unified surface by a group of polynomials with the fourth or less degree with respect to parameters u and v, and paths of a cutting tool to machine the unified surface are calculated by using the polynomials. According to this method, the solutions can be obtained arithmetically, and points on the unified curved surface expressed in the coordinate system (u, v) can be converted into values in the rectangular coordinate system (x, y, z) speedily and vice versa. However, curved surfaces are generally defined in forms of spline, B-spline, nubus, bezier, etc. and are not always defined by polynomials, and therefore, in order to carry out calculation control in the above method using expressions in other forms, some conversion is necessary.
In order to solve this problem, the applicant further disclosed, in Japanese Patent No. 2824424, a three-dimensional machining method wherein a plurality of curved surfaces are defined by a set of rational functions with respect to parameters u and v, and intersections which are necessary for machining are calculated by using the set of rational functions. The calculation according to this method is to figure out the solutions of the rational functions, and according to this method, any forms of expressions to define curved surfaces can be unified into a set of rational functions with respect to parameters u and v. Thereby, the calculation time can be shortened, and the accuracy of machining can be improved.
Nowadays, however, more kinds of forms are adopted to define curved surfaces, and there are cases of defining curved surfaces by analytic functions which are no longer expressions. In other words, there are cases that a plurality of curved surfaces cannot be defined by a set of rational functions.
An object of the present invention is to provide a three-dimensional machining method wherein various kinds of functions to define curved surfaces can be taken in and unified into a set of functions, and speedy calculation for machining can be carried out.
Another object of the present invention is to provide a storage medium stored with a three-dimensional machining control program adopting the above method.
In order to attain the objects, in a three-dimensional machining method according to the present invention, functions in a plurality of forms which express a plurality of curved surfaces and curves are received; it is judged whether solutions of the functions can be figured out by an algebraic method or an analytic method; the solutions are calculated by an algebraic method or an analytic method depending on the judgement; and the plurality of curved surfaces are defined by a set of functions with respect to parameters u and v.
A curved surface is defined by a continuous function with respect to parameters u and v, and a curve is defined by a continuous function with respect to S(u, v). Such a curved surface or a curve may be defined by an expression such as a polynomial or may be defined by a standard S(u, v) not by an expression. According to the present invention, when curved surfaces and curves are expressed by any standards S(u, v)=f(u, v), the points of intersection, the points of contact and the curves of intersection, etc. between the curved surfaces and curves are calculated directly, whereby the accuracy of the calculation is improved. Since this is executed to general continuous functions, needless to say, curved surfaces and curves defined by expressions can be handled in this way.
Calculating intersections means calculating the solutions of equations. The solution of an equation expressed by an analytic function can be figured out either by an algebraic method or an analytical method. If the solution can be figured out from an equation, an algebraic method is adopted. With respect to polynomials in the fourth or less degree, the solutions can be figured out by an algebraic method. On the other hand, if the solution cannot be figured out by an algebraic method, an analytical method is adopted. According to the present invention, it is possible to handle various kinds of functions.
At present, curved surfaces and curves are defined by functions in various forms; according to the present invention, however, it is possible to handle these functions together directly. Conventionally, various kinds of functions to define curved surfaces and curves are generally converted into functions in the same form (for example, nurbus, spline or the like) before calculation of intersection, and the accuracy of the calculation is not high. On the other hand, according to the present invention, various kinds of functions are handled directly and unified into a set of functions, and thereby, curved surfaces and curves defined by the set of functions are accurate.
According to the method disclosed by Japanese Patent No. 2824424, functions in the forms of nurbus, spline, bezier, etc. can be unified into a set of rational functions. The present invention is to unify general continuous functions, that is, to extend the range to which the technique disclosed by the patent is applicable.